Distributions and Power of Optimal Signal-Detection Statistics in Finite Case
Distributions and Power of Optimal Signal-Detection Statistics in Finite Case
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DOI：
10.1109/tsp.2020.2967179
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发表时间：
2020-01
影响因子：
5.4
通讯作者：
Hong Zhang;Jiashun Jin;Zheyang Wu
中科院分区：
文献类型：
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作者：
Hong Zhang;Jiashun Jin;Zheyang Wu
对于通过一组$n$输入$p$值来检测弱信号和稀疏信号，当$n$趋于无穷大时，高阶批评(HC)型统计量、Berk-Jones(B-J)型统计量和Phi散度统计量具有等价的渐近最优性。然而，它们在实际数据分析中可能具有显著不同的性能，其中$n$总是有限的，甚至是非常小的。为了在更广泛的背景下解决这个问题，本文引入了一族通用的拟合优度统计量，称为gGOF，它统一了包括这些最优统计量在内的广泛的信号检测统计量。在任意I.I.D.条件下，提供了gGOF统计量分布的有效而精确的解析计算。零假设和替代假设的连续模型。在此基础上，一项系统的功率研究表明，在有限的情况下，信号的数量往往比信号的比例更相关。对于相对较稀疏和较密集的信号，HC和反向HC分别具有优势，而B-J则更稳健。给出了基于广义线性模型的gGOF应用于数据分析的一般框架。在基于SNP集的克隆氏病全基因组关联研究中的应用表明，这些最优统计量在检测具有弱SNP效应的新疾病基因方面具有很好的潜力。这些计算已经在R包SetTest中实现，并在CRAN上发布。
For detecting weak and sparse signals by a set of $n$ input $p$-values, the Higher Criticism (HC) type statistics, the Berk-Jones (B-J) type statistics, and the phi-divergence statistics have the equivalent asymptotic optimality as $n$ goes to infinity. However, they can have significantly different performance in practical data analysis, where $n$ is always finite and even very small. To address this problem in a broader context, this paper introduces a general family of goodness-of-fit statistics, called the gGOF, which unifies a broad signal-detection statistics including these optimal ones. Efficient and accurate analytical calculations for the distributions of the gGOF statistics are provided under arbitrary i.i.d. continuous models of the null and the alternative hypotheses. Based on that, a systematic power study reveals that in finite case, the number of signals is often more relevant than the signal proportion. The HC and the reverse HC have advantages for relatively sparser and denser signals, respectively, while the B-J is more robust. A general framework is given to apply the gGOF into data analysis based on the generalized linear models. An application to the SNP-set based genome-wide association study (GWAS) for Crohn's disease shows that these optimal statistics have a good potential for detecting novel disease genes with weak SNP effects. The calculations have been implemented into an R package SetTest and published on the CRAN.